Measuring an angular displacement of a test object by reflecting a beam of light from the test object and measuring the beam deflection corresponding to the angular displacement is well known in the art. The basic principles of this method are shown on FIG. 1. An incident light beam 102 is reflected from a surface 112 to provide a reflected beam 114. If the angle of surface 112 changes, e.g., to align with dotted line 122, incident light beam 102 would be reflected along path 124. If the angular displacement of the reflective surface is ε, the corresponding difference in reflected beam direction is 2ε, which follows from the geometry of FIG. 1 and the reflection law (θi=θr).
It is also known in the art to measure angular displacement using optical systems that employ diffraction instead of or in addition to reflection. For example, U.S. Pat. No. 4,330,212 considers illumination of a diffraction grating on a test object. Changes in the position of the resulting diffraction pattern correspond to angular displacement of the test object. For example, a roll (rotation about the grating surface normal) of the test object will provide a corresponding roll of the diffraction pattern. A similar approach is also considered in U.S. Pat. No. 7,110,103.
In these references, diffraction is exploited to provide a pattern having multiple spots as opposed to a single reflected beam. Such a multiple spot pattern can provide information on angular displacements that cannot be measured with a single beam approach, such as rotation about the surface normal of the test object.
For the configuration of FIG. 1, the displacement of the reflected beam on a detector is 2εL, assuming a reflected beam working distance of L from the test object to the detector. In some applications, such as space based gravitational wave sensors, it is simultaneously required to provide very high angular sensitivity in combination with a relatively limited working distance L. In such cases, it can be difficult or even impossible to meet the combined sensitivity and working distance requirements, thereby requiring an undesirable design compromise.
Accordingly, it would be an advance in the art to provide optical measurement of angular displacement having improved angular sensitivity.